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本文分析研究了升力和滚转速率变化对弹头命中点的影响。假设滚转速率曲线可以用一系列直线段来逼近,则积分在小攻角时弹头受月球运动影响的运动方程。每一直线段出现在十分短的时间内,在这段时间内可以假定弹道特性为一常数。这一结果是一隐解,它表明,偏离零升力情况的合成命中偏差是零升力弹道特性和滚转速率曲线的函数。从这一通解导得在任意初始的和最后的滚转速率之间,一段线性变化的滚转速率变化对命中点的影响。文中提出了两种特殊情况:1.在两个数值大而符号相反的滚转速率间,过零滚转的情况。2.在任意两个滚转速率间,滚转加速度是无限大的情况。本文举例讨论了一段按线性变化的滚转速率问题,并将它和用六自由度弹道模拟所得的结果作比较。比较结果,两者之差一般在5％以内,没有一个差超过13％。
This paper analyzes the impact of lift and roll rate changes on the warhead hit point. Assuming that the roll rate curve can be approximated by a series of straight line segments, the equation of motion of the projectile affected by lunar motion at small angles of attack is integrated. Each straight line segment appears in a very short period of time, during which time it can be assumed that the trajectory characteristics are constant. This result is a covert solution that shows that the resultant hysteresis deviation from zero lift is a function of the zero lift trajectory and the roll rate curve. From this general solution, the influence of a linearly varying roll rate change on the hitting point between any initial and final roll rate is derived. Two special cases are proposed in this paper: 1. Zero roll-over between two large and opposite roll rates. 2. Between any two roll rates, roll acceleration is infinitely large. This article gives an example of a roll rate problem that varies linearly and compares it to the results obtained with a six-degree-of-freedom ballistic simulation. According to the comparison results, the difference between the two is generally within 5%, none of which exceeds 13%.